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Hardy-Lieb-Thirring inequalities for eigenvalues of Schrödinger operatorsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2007 (English)Doctoral thesis, comprehensive summary (Other scientific)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Stockholm: KTH , 2007. , p. vii, 28
##### Series

Trita-MAT. MA, ISSN 1401-2278 ; 07:03
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:kth:diva-4344ISBN: 978-91-7178-626-5 (print)OAI: oai:DiVA.org:kth-4344DiVA, id: diva2:11908
##### Public defence

2007-05-09, Sal F3, KTH, Lindstedtsvägen 26, Stockholm, 09:00
##### Opponent

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt467",{id:"formSmash:j_idt467",widgetVar:"widget_formSmash_j_idt467",multiple:true});
##### Supervisors

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#####

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##### Note

QC 20100708Available from: 2007-04-25 Created: 2007-04-25 Last updated: 2010-07-08Bibliographically approved
##### List of papers

This thesis is devoted to quantitative questions about the discrete spectrum of Schrödinger-type operators.

In Paper I we show that the Lieb-Thirring inequalities on moments of negative eigen¬values remain true, with possibly different constants, when the critical Hardy weight is subtracted from the Laplace operator.

In Paper II we prove that the one-dimensional analog of this inequality holds even for the critical value of the moment parameter. In Paper III we establish Hardy-Lieb-Thirring inequalities for fractional powers of the Laplace operator and, in particular, relativistic Schrödinger operators. We do so by first establishing Hardy-Sobolev inequalities for such operators. We also allow for the inclu¬sion of magnetic fields.

As an application, in Paper IV we give a proof of stability of relativistic matter with magnetic fields up to the critical value of the nuclear charge.

In Paper V we derive inequalities for moments of the real part and the modulus of the eigen¬values of Schrödinger operators with complex-valued potentials.

1. On Lieb-Thirring inequalities for Schrödinger operators with virtual level$(function(){PrimeFaces.cw("OverlayPanel","overlay11903",{id:"formSmash:j_idt519:0:j_idt523",widgetVar:"overlay11903",target:"formSmash:j_idt519:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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3. Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators$(function(){PrimeFaces.cw("OverlayPanel","overlay11905",{id:"formSmash:j_idt519:2:j_idt523",widgetVar:"overlay11905",target:"formSmash:j_idt519:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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5. Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials$(function(){PrimeFaces.cw("OverlayPanel","overlay11907",{id:"formSmash:j_idt519:4:j_idt523",widgetVar:"overlay11907",target:"formSmash:j_idt519:4:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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